As is well known, in the playing of pool, snooker, billiards, or similar games, it is necessary for the player to propel a cue ball along an appropriate direction to establish contact with an object ball at a position such that the latter will travel in the desired direction. More particularly, using as an example the playing of pool, the desired objective of impelling an object ball into a pocket essentially involves four prerequisites. First, the correct target (not necessarily the pocket itself) for the object ball must be chosen. Secondly, based on the target position, an accurate estimate of the object ball-cue ball contact point must be made. In the third place, the correct point of aim for the cue ball direction of travel must be determined to insure that the required contact point is encountered. Finally, an accurate stroke of the cue in establishing the appropriate direction of the cue ball must be made.
All of these prerequisites have been established primarily in the past by a trial and error method. For example, the "target" is generally considered by pool players, as the center of the pocket and, in turn, the contact point is established by mentally constructing a line from the center of the pocket through the center of vertical axis of the object ball. In turn, the point of aim is established by an imaginary line parallel to that of the contact point depending upon the amount of lateral motion of the object ball required and the accurate stroke is provided by trial and error practice. All of these have necessitated for the most part an extensive period of time before any proficiency in the playing of pool can be established.
The foregoing is, in and of itself, an oversimplification for as well known to any expert in the playing of pool, if a second "key" ball is placed adjacent an object ball with the two having contact established at the desired contact point in accordance with the above-stated principles, if a cue ball hits the "key" ball left of center, the travel or trajectory of the object ball will be thrown off to the right and to the contrary, if the cue ball contacts the "key" ball on its right side, the object ball will be thrown off line to the left. Such phenomenom is generally referred to by pool players as "throw" but few players realize that a corresponding phenomenom also occurs when a cue ball directly contacts an object ball without the intervening disposition of the key ball. As a consequence, a careful study of the travel of a cue ball and the impelled object ball indicated the error in the previously stated principle of establishing a contact point by drawing an imaginary line from the pocket through the vertical axis or center of the object ball.
Thus, any pool player who desires to become proficient must be aware of this basic "throw" phenomenon and be able to estimate the correct "target" in order to correctly locate the desired contact point on the object ball and, in turn, the point of aim. Obviously, it is also necessary that any player who is to become proficient must be capable of precise manipulation of the cue in order to achieve the proper stroke.